In general, navigation involves determining an object's location and/or orientation within a reference frame. Positioning systems are sometimes used for navigation. Positioning systems typically facilitate determination of an entity's location by transmitting signals from a set of transmitters having known (though not necessarily fixed) locations. For example, suitable signals may be transmitted from satellites, mobile phone towers, or Wi-Fi access points. The global positioning system (GPS) is an example of a satellite-based positioning system. When received by a suitable receiving device (e.g., a GPS receiver), the signals transmitted by a positioning system permit the receiving device to determine its location via triangulation, trilateration, or other suitable location-detection technique. In areas where the positioning signals transmitted by a positioning system are not reliably received, determining an object's position via the positioning system may be difficult or impossible.
Inertial navigation systems are also used for navigation. In contrast to a positioning system, an inertial navigation system (INS) determines an object's location based on a trusted initial location and data collected from one or more inertial measurement units (IMUs). An IMU determines the acceleration of an object and changes in the orientation of the object based on measurements provided by one or more accelerometers and/or gyroscopes physically connected to the object. An INS uses dead reckoning (a state estimation technique) to estimate the location and velocity of the object based on the acceleration and orientation measurements obtained from the IMU(s). In particular, after establishing an initial trusted location, the INS integrates the measurements provided by the IMU(s) to estimate the object's velocity and position as the object moves. Errors in the INS's estimate of the object's location generally increase over time due to the integration of uncompensated errors in the measurements obtained from the IMU(s), a phenomenon which is referred to herein as “time-dependent drift” or simply “drift.” During long excursions, drift can lead to significant errors in the estimated position of the object. The rate of drift can be reduced by performing zero-velocity updates (ZUPTs) during times when the IMU(s) are stationary. However, performing a ZUPT is often impractical, because the object is often not stationary, and placing the object in a stationary state is often infeasible.
A distributed spatial sensor, (e.g., a fiber optic shape sensor (FOSS)), is a third type of sensor that can measure the spatial positions and angular positions (e.g., orientations) of portions of a flexible cable or fiber (e.g., an optical fiber), and the shape of the flexible cable or fiber. Some fiber optic shape sensors obtain these measurements by using one or more fiber cores and an optical frequency domain reflectometer that transmits light to and receives reflected light from the optical fiber cores. In this way, the FOSS can measure the distributed strain on the fiber cores, which can be used to determine the position and shape of the optical fiber.
Fiber optic shape sensors with relatively short optical fibers can be used in a variety of medical instruments, including catheters, endoscopes, arthroscopes, colonoscopes, laparoscopes, and balloon catheters. With such instruments, the measurements obtained by the FOSS can be used to determine the location of the tip of the instrument inside the patient's body, the path of the instrument through the patient's body, etc. This information can be used to improve outcomes for related medical procedures, including catheterization, endoscopy, arthroscopy, colonoscopy, laparoscopy, and angioplasty.
For conventional distributed spatial sensors, imperfections in sensor calibration and noise in the measurement data can lead to errors in the sensor's measurements of position and shape. Some conventional long-length fiber optic shape sensors measure their shape and end-point position with an error of approximately 0.5% to 1.0% of the length of the optical fiber. The magnitudes of such errors generally grow larger as the length of the optical fiber increases, and can eventually reach unacceptable levels for some applications involving very long fiber lengths. Also, conventional FOSS may not provide accurate measurements of position and shape if the optical fiber experiences a significant, rapid change in its shape or state of strain while the measurements are being obtained.